Hi, you definitely can take them, and probably on the plane with you in a small carrier.
What I’d suggest to start is to do a search of the forum with keywords airplane, travel, flying. There have been many posts in the past about air travel, even internationally. They are older posts and read-only, so don’t reply to any there. But many may have links to airline info. sites that will give you more detailed info.
The only problem is the rapid changes in travel regulations overall. Whatever you find in posts you will need to confirm is still the case. Another way to go is to contact the airline you know you’re taking and peruse their website or call their customer service. They can tell you the most current options for flying, the costs, and whether you can take the bunnies in a carrier with you in the cabin or not.
It doesn’t sound like your folks will be able to get them boarded well, even if they care for them. You can also contact a local rescue, or the House Rabbit Society, and see if you can find people who might drive them for you. Sometimes bunnies are driven by a few people cross country when they are being adopted. Not sure of the cost. Your best bet is talking to the airlines you’re using, or even a different airlines that goes to your destination. It’s work, but been done.